Weight Equation

Gives the gravitational force on a mass near Earth's surface. Weight is what a scale reads when the object is in free space (no acceleration); it equals mg where g ≈ 9.8 m/s².

Any problem that requires the gravitational force on an object near a planet's surface. Weight appears as a force component in free-body diagrams for inclines, Atwood machines, elevators, and fluid problems.

g varies with altitude and planet; use the universal gravitation formula (F = GMm/r²) when height is not negligible compared to Earth's radius. Weight is not the same as apparent weight — in an accelerating frame, the normal force differs from mg.

Confusing mass (kg) with weight (N) — they are related but different quantities. Using g = 10 m/s² when the problem specifies 9.8 or 9.81. Forgetting that weight acts downward; sign errors on incline problems arise from not projecting mg along the correct axis.

• newtons three laws

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